A histone deacetylase (HDAC) inhibitor is a class of drug that interferes with the function of HDAC, an enzyme that hides HIV within inactive CD4 cells. These drugs are normally used to treat seizures and other nervous system problems but have been found to work against HIV. The purpose of this study is to investigate the efficacy of valproic acid (VPA), an HDAC inhibitor, in treating HIV infected adults using anti-HIV drugs.